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We introduce power term polynomial algebra, a representation language for Boolean formulae designed to bridge conjunctive normal form (CNF) and algebraic normal form (ANF). The language is motivated by the tiling mismatch between these…
The Boolean satisfiability (SAT) problem lies at the core of many applications in combinatorial optimization, software verification, cryptography, and machine learning. While state-of-the-art solvers have demonstrated high efficiency in…
Supervised fine-tuning (SFT) is a common method to enhance the tool calling capabilities of Large Language Models (LLMs), with the training data often being synthesized. The current data synthesis process generally involves sampling a set…
The recently proposed Conformer architecture which combines convolution with attention to capture both local and global dependencies has become the \textit{de facto} backbone model for Automatic Speech Recognition~(ASR). Inherited from the…
Autoformalization addresses the scarcity of data for Automated Theorem Proving (ATP) by translating mathematical problems from natural language into formal statements. Efforts in recent work shift from directly prompting large language…
In this paper, we investigate the problem of synthesizing resilient supervisors against combined actuator and sensor attacks, for the subclass of cyber-physical systems that can be modelled as discrete-event systems. We assume that the…
Shapley values, originating in game theory and increasingly prominent in explainable AI, have been proposed to assess the contribution of facts in query answering over databases, along with other similar power indices such as Banzhaf…
The realizability problem in requirements engineering is to determine the existence of an implementation that meets the given formal requirements. A step forward after realizability is proven, is to construct such an implementation…
We study the problem of verification and synthesis of robust control barrier functions (CBF) for control-affine polynomial systems with bounded additive uncertainty and convex polynomial constraints on the control. We first formulate robust…
Dominant areas of computer science and computation systems are intensively linked to the hypercube-related studies and interpretations. This article presents some transformations and analytics for some example algorithms and Boolean domain…
We will study some important properties of Boolean functions based on newly introduced concepts called Special Decomposition of a Set and Special Covering of a Set. These concepts enable us to study important problems concerning Boolean…
Neural Control Barrier Functions (NCBFs) have shown significant promise in enforcing safety constraints on nonlinear autonomous systems. State-of-the-art exact approaches to verifying safety of NCBF-based controllers exploit the…
Reactive synthesis is the process of generating correct controllers from temporal logic specifications. Classical LTL reactive synthesis handles (propositional) LTL as a specification language. Boolean abstractions allow reducing LTLt…
Many constraint satisfaction and optimisation problems can be solved effectively by encoding them as instances of the Boolean Satisfiability problem (SAT). However, even the simplest types of constraints have many encodings in the…
Automatic synthesis from a given specification automatically constructs correct implementation. This frees the user from the mundane implementation work, but still requires the specification. But is specifying easier than implementing? In…
We study the complexity of Boolean constraint satisfaction problems (CSPs) when the assignment must have Hamming weight in some congruence class modulo M, for various choices of the modulus M. Due to the known classification of tractable…
Stochastic Boolean Function Evaluation is the problem of determining the value of a given Boolean function f on an unknown input x, when each bit of x_i of x can only be determined by paying an associated cost c_i. The assumption is that x…
With the emerging applications that involve complex distributed systems branching-time specifications are specifically important as they reflect dynamic and non-deterministic nature of such applications. We describe the expressive power of…
Schaefer's theorem is a complexity classification result for so-called Boolean constraint satisfaction problems: it states that every Boolean constraint satisfaction problem is either contained in one out of six classes and can be solved in…
This paper proposes an algorithm for deciding consistency of systems of Boolean equations in several variables with co-efficients in the two element Boolean algebra $B_{0}=\{0,1\}$ and find all satisfying assignments. The algorithm is based…